# What is the GCF of 16 and another integer?

## Question:

What is the GCF of 16 and another integer?

## Greatest Common Factor

The Greatest Common Factor (GCF) or Greatest Common Divisor (GCD) {eq}d {/eq} of two integers {eq}a {/eq} and {eq}b {/eq} is the biggest or largest integer that can divide into (or evenly divide) both {eq}a {/eq} and {eq}b {/eq}. This is usually written as

{eq}\begin{align} \text{gcd}(a,b) ****= d. \end{align} {/eq}

where {eq}a {/eq} and {eq}b {/eq} are relatively prime if and only if {eq}\text{gcd}(a.b) = 1. {/eq}

## Answer and Explanation:

SInce {eq}16 = 2^4, {/eq} its only divisors are powers of 2 of the form {eq}2^k,\; k=0, 1, 2, 3, 4, {/eq} more clearly: 1, 2, 4, 8, and 16.

Hence,...

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